Problem 1: The economy has a representative consumer and a representative produer. A. The consumer's utility function is given by: 00 Ut = Bu(Ct+s) s=0 The consumer has an income in period r: Y = f(K) which he will expend on consumption (C) or to buy new capital to be used during the next period (Kt+1). Find the solution of the consumer's utility maximization problem given the budget constraint and two additional constraints: C 0 and K++1 20. The decision variables in the consumer problem are C and Kt+1- B. Find the profit-maximizing level of capital demand if the firm has to pay a return on capital of (1 + R), subject to the production function : Y = f(K). C. Given the above problems of the consumer and the firm, show that they can be reduced to a traditional Euler equation when the rate of return on capital is equal to the interest rate. D. Apply the above problems with examples of the utility and production functions.